Modified 5-point fractional formula with Richardson extrapolation

Iqbal M. Batiha; Shameseddin Alshorm; Iqbal Jebril; Amjed Zraiqat; Zaid Momani; Shaher Momani

doi:10.3934/math.2023480

Modified 5-point fractional formula with Richardson extrapolation

Iqbal M. Batiha
, Shameseddin Alshorm
, Iqbal Jebril
, Amjed Zraiqat
, Zaid Momani
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
The University of Texas at Arlington
University of Jordan

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

In this paper, we establish a novel fractional numerical modification of the 5-point classical central formula; called the modified 5-point fractional formula for approximating the first fractional-order derivative in the sense of the Caputo operator. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.

Original language	English
Pages (from-to)	9520-9534
Number of pages	15
Journal	AIMS Mathematics
Volume	8
Issue number	4
DOIs	https://doi.org/10.3934/math.2023480
State	Published - 2023

Keywords

Caputo derivative
Lagrange interpolating polynomial
Richardson extrapolation
Riemann-Liouville fractional derivative and integral

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10.3934/math.2023480

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title = "Modified 5-point fractional formula with Richardson extrapolation",

abstract = "In this paper, we establish a novel fractional numerical modification of the 5-point classical central formula; called the modified 5-point fractional formula for approximating the first fractional-order derivative in the sense of the Caputo operator. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.",

keywords = "Caputo derivative, Lagrange interpolating polynomial, Richardson extrapolation, Riemann-Liouville fractional derivative and integral",

author = "Batiha, \{Iqbal M.\} and Shameseddin Alshorm and Iqbal Jebril and Amjed Zraiqat and Zaid Momani and Shaher Momani",

note = "Publisher Copyright: {\textcopyright} 2023 the Author(s), licensee AIMS Press.",

year = "2023",

doi = "10.3934/math.2023480",

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T1 - Modified 5-point fractional formula with Richardson extrapolation

AU - Batiha, Iqbal M.

AU - Alshorm, Shameseddin

AU - Jebril, Iqbal

AU - Zraiqat, Amjed

AU - Momani, Zaid

AU - Momani, Shaher

PY - 2023

Y1 - 2023

N2 - In this paper, we establish a novel fractional numerical modification of the 5-point classical central formula; called the modified 5-point fractional formula for approximating the first fractional-order derivative in the sense of the Caputo operator. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.

AB - In this paper, we establish a novel fractional numerical modification of the 5-point classical central formula; called the modified 5-point fractional formula for approximating the first fractional-order derivative in the sense of the Caputo operator. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.

KW - Caputo derivative

KW - Lagrange interpolating polynomial

KW - Richardson extrapolation

KW - Riemann-Liouville fractional derivative and integral

UR - https://www.scopus.com/pages/publications/85148210578

U2 - 10.3934/math.2023480

DO - 10.3934/math.2023480

M3 - Article

AN - SCOPUS:85148210578

SN - 2473-6988

VL - 8

SP - 9520

EP - 9534

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 4

ER -

Modified 5-point fractional formula with Richardson extrapolation

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Keywords

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